4D printing of fully programmable sheets of digital metamaterials

Advances in 3D printing technology now enable the precise positioning of microscopic material voxels to form complex structures. Combined with emerging multi-material capabilities and printable responsive materials, this opens new possibilities for digital composite materials and 3D printing of shape-transforming structures, a process known as 4D printing. Building upon these advancements, we present a novel methodology for designing and fabricating digitized 4D-printed shape-transforming sheets. We 3D print responsive continuous sheets composed of two layers, each consisting of active and passive voxels meticulously positioned to form thin structures that transform on demand. Our approach addresses a long-standing challenge in the field: the independent and simultaneous programming of lateral geometry and intrinsic curvature. This unprecedented control over the resulting shape unlocks new opportunities in synthetic shape-morphing materials. We provide a general algorithmic approach that is material-agnostic and enables systematic design of shape transformations with potential capabilities for programmable mechanical properties and multi-actuation-mode systems and applications in soft robotics and deployable structures.